IDEAS home Printed from https://ideas.repec.org/a/bla/jorssb/v70y2008i1p265-286.html
   My bibliography  Save this article

Non‐parametric small area estimation using penalized spline regression

Author

Listed:
  • J. D. Opsomer
  • G. Claeskens
  • M. G. Ranalli
  • G. Kauermann
  • F. J. Breidt

Abstract

Summary. The paper proposes a small area estimation approach that combines small area random effects with a smooth, non‐parametrically specified trend. By using penalized splines as the representation for the non‐parametric trend, it is possible to express the non‐parametric small area estimation problem as a mixed effect model regression. The resulting model is readily fitted by using existing model fitting approaches such as restricted maximum likelihood. We present theoretical results on the prediction mean‐squared error of the estimator proposed and on likelihood ratio tests for random effects, and we propose a simple non‐parametric bootstrap approach for model inference and estimation of the small area prediction mean‐squared error. The applicability of the method is demonstrated on a survey of lakes in north‐eastern USA.

Suggested Citation

  • J. D. Opsomer & G. Claeskens & M. G. Ranalli & G. Kauermann & F. J. Breidt, 2008. "Non‐parametric small area estimation using penalized spline regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 265-286, February.
  • Handle: RePEc:bla:jorssb:v:70:y:2008:i:1:p:265-286
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9868.2007.00635.x
    Download Restriction: no

    References listed on IDEAS

    as
    1. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, July - De.
    2. Gerda Claeskens, 2004. "Restricted likelihood ratio lack‐of‐fit tests using mixed spline models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(4), pages 909-926, November.
    3. Ciprian M. Crainiceanu & David Ruppert, 2004. "Likelihood ratio tests in linear mixed models with one variance component," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 165-185, February.
    4. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, July - De.
    5. Helen Parise & M. P. Wand & David Ruppert & Louise Ryan, 2001. "Incorporation of historical controls using semiparametric mixed models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 50(1), pages 31-42.
    6. Brent A. Coull & David Ruppert & M. P. Wand, 2001. "Simple Incorporation of Interactions into Additive Models," Biometrics, The International Biometric Society, vol. 57(2), pages 539-545, June.
    7. Jiming Jiang & P. Lahiri, 2006. "Mixed model prediction and small area estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(1), pages 1-96, June.
    8. Ciprian Crainiceanu & David Ruppert & Gerda Claeskens & M. P. Wand, 2005. "Exact likelihood ratio tests for penalised splines," Biometrika, Biometrika Trust, vol. 92(1), pages 91-103, March.
    9. Peter Hall & Tapabrata Maiti, 2006. "On parametric bootstrap methods for small area prediction," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(2), pages 221-238, April.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:jorssb:v:70:y:2008:i:1:p:265-286. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wiley Content Delivery). General contact details of provider: http://edirc.repec.org/data/rssssea.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.